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How do you graph #7/3x <7#?

Answer 1

See a solution process below:

Multiply each side of the inequality by #color(red)(3)/color(blue)(7)# to solve for #x# while keeping the inequality balanced:

#color(red)(3)/color(blue)(7) xx 7/3x < color(red)(3)/color(blue)(7) xx 7#

#cancel(color(red)(3))/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))/color(red)(cancel(color(black)(3)))x < color(red)(3)/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))#

#x < 3#

To graph this we will draw a vertical line at #3# on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the left side of the line because the inequality operator contains a "less than" clause:

graph{x < 3 [-10, 10, -5, 5]}

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Answer 2

Nathan Axel

To graph the inequality ( \frac{7}{3}x < 7 ), you first graph the line ( y = \frac{7}{3}x ) (which has a slope of ( \frac{7}{3} )). Then, since the inequality sign is "<", the region below the line ( y = \frac{7}{3}x ) (excluding the line itself) represents the solution.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you graph #7/3x &lt;7#?

How do you graph #7/3x <7#?